In a Shirt factory, there are three processes named A,B, and C.They manufactures 25%, 35%, 40% of production respectively.of these 5%, 4%, 2% are defective.What is the probability the randomly selected shirt is of the defective one produced by process C?Options 1669 2869 2769
Question
In a Shirt factory, there are three processes named A,B, and C.They manufactures 25%, 35%, 40% of production respectively.of these 5%, 4%, 2% are defective.What is the probability the randomly selected shirt is of the defective one produced by process C?Options 1669 2869 2769
Solution
To solve this problem, we need to use the concept of conditional probability.
Step 1: Identify the given probabilities.
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Probability of a shirt being manufactured by process A, P(A) = 25% = 0.25
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Probability of a shirt being manufactured by process B, P(B) = 35% = 0.35
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Probability of a shirt being manufactured by process C, P(C) = 40% = 0.40
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Probability of a shirt being defective given it was manufactured by process A, P(D|A) = 5% = 0.05
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Probability of a shirt being defective given it was manufactured by process B, P(D|B) = 4% = 0.04
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Probability of a shirt being defective given it was manufactured by process C, P(D|C) = 2% = 0.02
Step 2: Calculate the total probability of a shirt being defective.
P(D) = P(A) * P(D|A) + P(B) * P(D|B) + P(C) * P(D|C) = 0.25 * 0.05 + 0.35 * 0.04 + 0.40 * 0.02 = 0.0125 + 0.014 + 0.008 = 0.0345
Step 3: Calculate the probability that a randomly selected defective shirt is produced by process C.
We use the formula for conditional probability: P(C|D) = P(D|C) * P(C) / P(D)
P(C|D) = 0.02 * 0.40 / 0.0345 = 0.008 / 0.0345 = 0.2318840579710145
So, the probability that a randomly selected defective shirt is produced by process C is approximately 0.232 or 23.2%.
None of the given options match this result.
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